Framework for solutions of the Boltzmann equation for ions of arbitrary mass

Abstract

We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by using appropriate quadratures to obtain the required matrix elements. We demonstrate an implementation using Burnett functions and benchmark the calculations using Monte-Carlo simulations. Even though the convergence in transport quantities is always good, the particle distributions did not always converge, highlighting that simple benchmarks can give misleading confidence in a choice of basis. We postulate a different basis, which avoids a spherical harmonic expansion, which is better suited to strong electric fields or sharp features such as low-energy attachment processes.

arXiv comment10 pages, 4 figures

References in corpus (7)

• A Monte Carlo simulation of ion transport at finite temperatures
• Kinetic Solvers with Adaptive Mesh in Phase Space
• Fully Coupled Simulation of the Plasma Liquid Interface and Interfacial Coefficient Effects
• Kinetic Theory of Positron-Impact Ionization in Gases
• An improved Monte Carlo study of coherent scattering effects of low energy charged particle transport in Percus-Yevick liquids
• Electron excitation and energy transfer rates for H2O in the upper atmosphere
• Ion velocity distribution functions in argon and helium discharges: detailed comparison of numerical simulation results and experimental data